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OK, here's one that'll get you thinking. Hell, it's had me thinking since Electronics 101 as a Junior in HIgh School (1985 - 1986 that was . . . )

The number .707 comes up often in math (It's actually .7071067811 ... but .707 will do for this brain twister). IE - consider the following formulas, and their relationship to one another:

Power = Voltage2 / Resistance

RMS Power = (Voltage x .707)2 / Resistance

Now, when you go and square .707, you get .500 which is pretty cool in and of itself, but then when you consider that RMS Power = Peak Power / 2, you also discover that you're really dealing with the same amount of "power" . . . just discussing it differently.

For example, let's say that we have an amplifier that can deliver 10 Volts AC (IE - a sine wave that measures 10 Volts at it's Peak) into a 2 Ohm resistive load. Let's solve for Power and RMS Power:

Power = (10 Volts)2 / 2 Ohms

Power = 100 / 2

Power = 50 Watts

RMS Power = (10 Volts x .707)2 / 2 Ohms

RMS Power = (7.07)2 / 2 Ohms

RMS Power = 50 / 2 Ohms

RMS Power = 25 Watts

Therefore, we've proved that 50 Watts "Peak" = 25 Watts RMS.

There are numerous mathematical equations at which the result is .707 . . . who can name a few?

Tony Candela - SMD Sales & Marketing
Email me at [email protected] to learn about becoming an SMD Partner!

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A 3db decrease in power ends up with the output voltage being reduced by a factor of 707. Useful trick to know when setting crossover points.

It's also the conversion factor from peak to peak (square wave) voltage to RMS(sine wave) voltage. Works great for setting amps with a DMM. Measure the rail voltage, do the conversion, adjust the gain accordingly, boom done. It's a bit more accurate then trying to use the traditional DMM method IMO. Especially in amps that are underrated and trying to adjust the gain to a preset number will end up with clipping in an attempt to get the desired output voltage

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The sine of 45 degrees is .707

idea22.jpg ALL CREDIT TO XX1 FOR DC BANNER 3178gvp.jpg

down rpping vanderbilt. 30 miles from victoria. i own the 3rd loudest setup here out of 3. but i did put together all 3 setups

strapping 2 amps together ? like bolting them next together? using bungy cables to hold them down? or wiring separate amps to each sub

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Qtc of .707 is a magic number for best response in a sealed enclosure.

Like cleansiera mentioned, it's also the Second-Order Butterworth, which is for max flat amplitude response.

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and the cosine . . .

you sir are correct :P

i love reading your stuff, even though it takes me a while and a couple hundred re reads to understand it.. haha

idea22.jpg ALL CREDIT TO XX1 FOR DC BANNER 3178gvp.jpg

down rpping vanderbilt. 30 miles from victoria. i own the 3rd loudest setup here out of 3. but i did put together all 3 setups

strapping 2 amps together ? like bolting them next together? using bungy cables to hold them down? or wiring separate amps to each sub

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